Interesting story you have there. Firstly, only you can make yourself happy and you are not responsible for anyone else’s happiness.
Secondly, having an affair when your partner is expecting, it’s a cliche and you have to accept that.
A lot of couples end in separation or divorce and it doesn’t make you a bad person. It might make you a better dad. You have to do what is right your yourself and your dependant.
I would suggest going and getting some counselling to at least get it off your chest and discuss your feeling about all aspects of the situation.
Don’t be so hard on yourself, you’ve made a mistake and a lot of people do, doesn’t mean you have to beat yourself up about it. But only you can decide what you want, there are clearly tough decisions to make in all aspects of your situation.
Get some help, you’re not alone!